# BCS theory for neutral fermions

As I understand it, Cooper pairs form between two fermions and are the cause of superconductivity. I was told by a teacher that the formation of Cooper pairs and BCS theory requires both fermions to be charged. But I also understand that Cooper pairs can form between two neutrons in neutron stars and neutrons are neutral particles. I asked the teacher the same question and they told me that it was because of pairing between the quark constituents of the neutron.

However, I have not been able to find any article or text that refers to this. In reading about BCS theory I have also not found any discussion on the fermions needing to be charged. Could someone refer me to any such text? Or help me understand what I am missing. I am new to the subject and asking questions as a novice.

The context of the discussion was that the teacher was saying that neutron star superconductivity and superfluidity required QED to be described. And I could not understand how QED could be applied to neutrons.

• Dec 29 '18 at 19:46

Neutral $$^3$$He atoms also pair to form a BCS-like superfluid. There has to be some source of an attractive force to cause the pairing, and in this case attractive pairing force comes from correlated fluctuations of the atoms' nuclear magnetic moments. I suppose that you can say that there is some electric charge causing the magnetic moments. In neutron stars, though, the pairing presumabley comes from the strong-force interactions -- so pairing does not always require an electromagnetic charge.